\(\left|x+5\right|=2x-18\)
\(\Rightarrow\left|x+5\right|-2x=-18\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5-2x=-18\left(đk:x+5\ge0\right)\\-\left(x+5\right)-2x=-18\left(đk:x+5< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x+5=-18\\-x-5-2x=-18\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=-18-5\\-3x-5=-18\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=-23\\-3x=-18+5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=-23\\-3x=-13\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=23\left(đk:x\ge-5\right)\\x=\dfrac{13}{3}\left(đk:x< -5\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=23\\x\in\varnothing\end{matrix}\right.\)
Vậy \(x=23\)
\(\left|x+5\right|=2x-18\)
+ ) \(\left|x+5\right|=x+5.\) Khi \(x+5\ge0\Leftrightarrow x\ge-5\)
\(\Leftrightarrow x+5=2x-18\)
\(\Leftrightarrow-x=-23\Leftrightarrow x=23\left(TM\right)\)
+ ) \(\left|x+5\right|=-x-5.\)Khi \(-x-5< 0\Leftrightarrow-x< 5\Leftrightarrow x>5\)
\(\Leftrightarrow-3x=-13\Leftrightarrow x=\dfrac{13}{3}\left(KTM\right)\)
Vậy ...
